In the current study, forty-two participants completed an IRAP with happy and fearful faces and words. Participants were divided in terms of whether they commenced with a history-consistent or a history-inconsistent block of trials. In addition, although participants were required to achieve the latency and accuracy performance criteria at the block level, participants were grouped according to whether or not they maintained the criteria at the trial-type level (over test blocks). Consistent with previous findings and the DAARRE model, there was evidence of both a STTDE and a DTTTE. However, both of these effects were moderated by other variables. Specifically, the difference between trial-types 1 and 4 was strongly significant for the group of participants who failed to maintain the criteria at the trial-type level, but it was not significant only for the group of participants who managed to maintain such performance across all trial-types. Furthermore, the difference between trial-types 2 and 3 was only significant for the group of participants who commenced the IRAP with a history-inconsistent block. While the findings were broadly consistent with the DAARRE model, the impact of block order and maintaining criteria at the trial-type level suggests that the model needs to be extended to accommodate these effects.
Let us first consider the impact of maintaining the criteria at the trial-type level on the STTDE. There was limited evidence for the STTDE for the group who maintained the criteria at the trial-type level, but a very clear STTDE for the group who did not. As noted previously, the vast majority of IRAP studies have focussed on performance criteria at the block level alone, and thus the current finding could be important in terms of informing future IRAP research. At this point, it seems important to consider a possible explanation for the impact of maintaining trial-type level criteria. As noted earlier, RFT distinguishes between Crel and Cfunc properties of stimuli, and the DAARRE model, more specifically, focusses on this distinction in the elements presented within an IRAP. The Crel properties refer to the “semantic” relationships between the label and target stimuli, whereas the Cfunc properties refer to the functional properties of the stimuli, such as valence or attentional effects.
If a participant’s performance on an IRAP was controlled largely by the Crel properties, then the IRAP would simply involve categorising the stimuli according to their semantic relations; indeed, all participants successfully did so when rating the stimuli without performance constraints (Table 1). Assuming that a participant has an appropriate history to complete such categorising, each trial-type might be considered broadly equal in difficulty. In contrast, if the Cfunc properties of the elements in an IRAP are involved, they may “interfere” with the control by the Crel properties and thus generate the observed differences between trial-types 1 and 4. If this view is correct, then maintaining the performance criteria at the trial-type level may be seen as indicating dominant control by the Crel properties of the IRAP. Or, more informally, participants who maintained the criteria were simply categorising happy faces with happy words, and fearful faces with fearful words, and this responding did not seem to be heavily influenced by the valence or emotional functions of stimuli, thereby producing roughly equal IRAP effects in trial-types 1 and 4 (i.e., they were more under Crel than Cfunc control). In contrast, failing to maintain the criteria at the trial-type level may indicate that the Cfunc properties interfered with Crel control. Or, more informally, participants who failed to maintain one or more performance criteria may have found it easier to respond positively (i.e., “true”) to two positive stimuli (maximal coherence) than to two negative stimuli (reduced coherence), thereby producing differential trial-type effects. This may be explained by the dynamic influence of the two types of contextual control that can take place differently for different people. Similar interpretations have been applied to explain clinical processes in the context of human psychological suffering (for a detailed discussion, see Harte et al., 2022).
Let us now consider the impact of block order on the DTTTE. While DIRAP scores for trial-type 2 were overall higher than for trial-type 3, this difference was specifically significant only for participants who started with the inconsistent block (i.e., the main effect was significant, but the only paired comparison that showed significance was for inconsistent-first participants). It is difficult to explain this difference based on Cfunc coherence alone, because the number of stimuli bearing positive and negative Cfunc properties is the same across these two trial-types. Namely, they both encompass one positive stimulus (as label in trial-type 2 and as target in trial-type 3) and one negative stimulus (as label in trial-type 3 and as target in trial-type 2). Note, also, that the Cfunc for both response options is negative in history-consistent blocks and positive in history-inconsistent blocks. In an attempt to explain the significant difference between trial-types 2 and 3 for participants who started with the inconsistent block, we will first draw on Kavanagh et al.’s (2019) explanation, which focussed on the spatial contiguity between the targets and the correct response options in each trial-type.
Kavanagh et al. (2019) noted that, in history-consistent blocks, for trial-type 2, the correct response option (e.g., “false”) bears a negative Cfunc which is coherent with the negative target (e.g., “fearful”); but for trial-type 3, it is incoherent with the positive target (e.g., “cheerful”). As such, responding correctly to trial-type 3 relative to 2 may be more difficult in the history-consistent block. In contrast, in history-inconsistent blocks, for trial-type 2, the correct response option (e.g., “true”) bears a positive Cfunc which is incoherent with the negative target; but for trial-type 3, it is coherent with the positive target. Consequently, responding correctly to trial-type 2 may be more difficult relative to trial-type 3 during the history-inconsistent block. Overall, therefore, responding correctly to trial-type 2 may be easier during consistent blocks and more difficult during inconsistent blocks, but the opposite is the case for trial-type 3 (i.e., more difficult during consistent blocks, but easier during inconsistent-blocks). If this analysis is correct, it would readily explain why the DIRAP score for trial-type 3 is less than the score for trial-type 2. That is, for trial-type 2, the functional overlap between target and correct response option is coherent during consistent blocks and incoherent during inconsistent blocks (thereby increasing the DIRAP score); but, for trial-type 3, there is incoherence between target and correct response option during consistent blocks, and coherence during inconsistent blocks (thereby decreasing the DIRAP score). The current finding indicates that this differential trial-type effect (the DTTTE) was only significant when participants commenced the IRAP with an inconsistent block, an effect that was not explored, and therefore not reported, by Kavanagh et al.
How might we explain this effect for block order? When participants commenced the IRAP with a history-consistent block, the overall context of the procedure, in terms of the Crel control, would be coherent with the participants’ previous verbal history. Their first contact with the procedure may therefore establish relatively strong control by both the label and target stimuli in terms of Crel properties. In contrast, for those participants who commenced with the history-inconsistent block, responding coherently with the Crel properties would have been punished and therefore other sources of coherence may have impacted their performance (assuming that, in general, participants had an extensive history of responding coherently in their natural environment). One such source of coherence would have been the overlap in the Cfunc properties of the spatially-contiguous target and correct response option for trial-type 3 (in a history-inconsistent block). Given the current findings, it seems that this initial source of coherence in the first block of the IRAP continued to impact performance throughout the procedure. In other words, participants who started with the history-inconsistent block may have developed a type of “nearest Cfunc coherence” response bias for trial-type 3, which only favoured performance in history-inconsistent blocks. This bias would be punished during subsequent history-consistent blocks for trial-type 3, which may explain the reduction in the DIRAP scores for trial-type 3 relative to trial-type 2. We are assuming here that the “nearest Cfunc coherence” response bias resurged during all subsequent history-inconsistent blocks for participants who started with this type of block.
Of course, this interpretation is post hoc and rather speculative, but it could be tested in subsequent research. For example, it would be interesting to examine the impact of specific instructions on such effects. In the current study, participants were required to learn to relate the stimuli through trial-and-error, because no specific instruction on how to relate the stimuli was provided. Perhaps, providing detailed instructions explaining that the first IRAP block would require responding in a manner that was incorrect (i.e., incoherent with prior verbal history) might undermine the order effect observed here. That is, such an instruction would render a history-inconsistent block coherent with the prior instructions to respond incoherently, thereby attenuating the “nearest Cfunc coherence” bias (see Finn et al., 2016).
One might assume that using words as targets and response options may have contributed to the coherence between these stimuli. However, Kavanagh et al. (2019) observed a very similar DTTTE to the one reported here, even though the IRAP configuration employed by Kavanagh et al. used pictures as targets (and words as response options). As noted previously, Kavanagh et al. did not analyse their data in terms of block order, but the overall pattern was similar (trial-type 2 larger than trial-type 3). Furthermore, it is also worth noting Kavanagh et al. employed relatively neutral stimuli (i.e., pens and non-emotional faces), and thus the differential trial-type effects they obtained might have been based more on orienting (e.g., attentional) rather than evoking (e.g., valence) functions (see Finn at al., 2018). As such, the pattern observed here appears to be generally consistent with previous studies (cf. Hussey & Drake, 2020).
Only two previously published studies, to our knowledge, have focussed on both the STTDE and the DTTTE (Kavanagh et al., 2019; Schmidt et al., 2021). The STTDE, specifically, has been consistently replicated across different domains, such as colour–colour over shape–shape (Finn et al., 2018), face–face over pen–pen (Kavanagh et al., 2019), happy-symbol–positive-word over fearful-symbol–negative-word (Perez et al., 2019); happy-face–happy-symbol over negative-emotion–negative-symbol (Bortoloti et al., 2019; see also Bortoloti et al., 2020), happy-face–preferred-icon over angry-face–indifferent-icon (Pinto et al., 2020); and opposing patterns of in-group over out-group positivity bias (Hughes et al., 2017). However, the current study was only the second to predict a priori both the STTDE and the DTTTE (the first being Schmidt et al., 2021), and these effects were indeed observed. Furthermore, the current study is the first to analyse the data at the individual level and, interestingly, not all the participants showed these two effects. In this context, it is important to understand that the type of Cfunc properties involved in a participant’s performance could, in principle, change the pattern of responding on the IRAP. For example, if the valence (i.e., evoking properties) of the faces tended to control responding, then a happiness superiority effect would be more likely; in contrast, if the salience (i.e., orienting functions) of specific features of the faces (e.g., wide-open eyes in fearful faces) tended to control responding, then a fear superiority effect would be more likely. In other words, a fear superiority effect for a particular individual should not be interpreted as “preferring” or “liking” fearful more than happy faces (see Hughes et al., 2018). According to the DAARRE model, it is the specific Cfunc properties of the stimuli (orienting versus evoking) that play an important role in determining the overall response patterns observed on the IRAP. These stimulus properties may well differ between participants based on their idiosyncratic pre-experimental histories. However, consistent with previous research (Bortoloti et al., 2019; Craig et al., 2014; Leppänen & Hietanen, 2004), a happiness superiority effect, in general, was observed in the current study, although this was moderated by maintaining the performance criteria at the trial-type level, which is very much a novel finding in the IRAP literature.
In line with Finn et al. (2019), the present study reported individual-participant data, thus supporting their call for such analyses in IRAP research (p. 434). The potential advantage in doing so may be exemplified when considering the impact of maintaining criteria on the STTDE. Specifically, for individual participants (Fig. 3), the vast majority of those who did not maintain the criteria showed a much larger DIRAP score for trial-type 1 relative to 4. Furthermore, only three of these 19 participants showed the opposite effect (trial-type 4 larger than 1). Although the frequency-based analyses did not indicate an association between maintaining criteria and the STTDE, the variance-based analyses did support a significant interaction. One likely reason is because the frequency-based analyses did not capture the relative magnitudes of the DIRAP scores, thus failing to reflect the impact of relatively large effects such as the five participants with the highest trial-type-1-minus-4 differences, who were all in the criteria-failing group. In effect, when participants do not maintain the performance criteria, their differential trial-type effects may tend to be larger (in the predicted direction) than when they do maintain the criteria. Analysing IRAP data both in terms of frequency and variance allows us to see such effects.
The current findings are broadly consistent with previous research that has drawn on the DAARRE model in highlighting the combined role of Crel and Cfunc properties in determining differential trial-type effects on the IRAP. Conceptually, this increasingly well-established finding seems to warrant a change in focus within RFT (Harte & Barnes-Holmes, 2024). Traditionally, in RFT, the relationship between entailed relations and the transformation of functions has frequently focussed on the extent to which establishing specific entailed relations allows for specific changes in the functional properties of the stimuli participating within those relations. For example, in many RFT studies a relational network may be established in which three stimuli are related to each other, for instance when A is trained as more than B, and B is trained as more than C. A specific functional property may then be established for one of the stimuli, such as an aversive (e.g., electric shock) function for C. Subsequently, the A stimulus may evoke an aversive reaction stronger than the reaction that was observed for the C stimulus, because A is derived as more than C (see, for example, Dougher et al., 2007). This approach focuses on the impact of the stimulus relations (Crel) on the functional properties (Cfunc) of the stimuli in a given network. In the current and related research, however, there is a greater focus on the impact of the functional properties of the stimuli on relating. More specifically, the coherence among the Cfunc properties of the stimuli within the network seems to interact with their Crel properties in a way that explains the responding patterns observed on the IRAP. On balance, recognising the impact of Cfunc properties on Crel properties does not mean that the “traditional” approach (i.e., from relation to function) was incorrect; both approaches can supplement each other (Harte & Barnes-Holmes, 2024).
We should also acknowledge that previous research has reported effects consistent with a function-to-relation approach, in which functional classes were shown to generate equivalence relations (e.g., Sidman et al., 1989; Smeets et al., 1997). Nevertheless, most of this research focused on demonstrating that functional classes may generate equivalence relations, but they did not indicate that the functional properties of the stimuli could affect the accuracy and latency of relational responding itself. The DAARRE model addresses the relative coherence among the Cfunc and Crel properties of the stimuli within a network on the IRAP, and this supports a more thorough analysis of the dynamic interplay between the relational and the functional properties of stimuli (Harte & Barnes-Holmes, 2024).
Adopting a relatively balanced focus between Crel and Cfunc properties, as we have suggested here, may serve to highlight potential commonalities with research on language in other domains. For example, semantics, as a subset of linguistics, has traditionally tended to focus on explanations of the formal structure of language, even when addressing the referencing relationships between linguistic expressions and concepts or categories (e.g., cf. Glynn, 2015; Rakhilina et al., 2022; Rosch, 1973). Broadly speaking, in RFT terms, this focus would be on the Crel properties of a semantic network. However, when language is viewed as an evolutionary feature of the human species (Pinker & Bloom, 1990), this calls for a focus on the psychological learning history of language across human development (i.e., how the specific properties of language are selected by the environment, both across and within generations), and thus on the pragmatics of language learning. The present findings emphasise the importance of the transformation of historically established psychological functions (Cfunc) of stimuli in arbitrarily applicable relational responding (under Crel control), as studied by RFT, in conceptualising meaning and categorisation, for it shows that the former impacts upon the latter.
In using merely descriptive adjectives (e.g., happy, fearful) with facial expressions assumed to be generally described as such (cf. Barrett et al., 2019), the task itself simply required participants to categorise attributes into their domains based on literal semantic equivalences. These mappings referred to emotional concepts that are presumedly not socially meaningful (e.g., in terms of race or gender), but the differences in the bare emotional value of stimuli influenced the emergence of differential trial-type effects. These effects may possibly be applied in research on socially sensitive issues, such as in-group and out-group biases in the context of social identities.
For instance, using evaluative adjectives (e.g.: honest, nice, friendly; nasty, aggressive, hostile), Hughes et al. (2017) asked Northern Irish participants from either community (Catholic or Protestant) to respond to four trial-types: Catholic–good, Catholic–bad, Protestant–good, Protestant–bad, using “True” and “False” as response options. On average, trial-types with a positive evaluative adjective were all significantly different from zero in the direction where the positive adjective had to be responded to as “True”, for both groups (i.e., both groups assessed their in-group and out-group as “good”). However, Catholic participants showed DIRAP scores in the Catholic–good trial-type that were higher than the Protestant–good trial-type, whereas Protestant participants showed DIRAP scores in the Protestant–good trial-type higher than the Catholic–good trial-type. Hughes et al. concluded that the IRAP revealed in-group favouritism in the absence of out-group derogation. One direction for future research would be to replicate the current study using socially loaded stimuli like those employed by Hughes et al. Would the effects reported by those researchers be moderated by the two variables found to be relevant in the current study?
Summary and concluding remarks
We henceforth abridge our analyses and key findings. The significant main effect for STTDE did not interact with block order, as a significant “happiness superiority effect” (trial-type 1 bigger than trial-type 4) was significant regardless of block order. STTDE also had a significant main effect when performance maintenance was concerned, but in that case it interacted significantly with whether or not participants maintained the performance criteria at the trial-type level. Specifically, there was very strong evidence for higher DIRAP scores in trial-type 1 relative to 4 for participants who failed to maintain at least one of the performance criteria in at least one trial-type, but there was no evidence for such difference for participants who maintained both performance criteria across all trial-types. This interaction was not reflected in the chi-square test because this analysis considered STTDE in a dichotomous way (i.e., 1 > 4 or 4 > 1), and therefore it could not capture the magnitudes of the scores’ differences. A visual inspection of the Finn graphs in Fig. 3 (upper-right panel) illustrates that point.
A significant main effect for DTTTE (trial-type 2 bigger than trial-type 3) did not interact with block order, but the categorical analyses captured a significant association whereby DTTTE effects depended on block order. This was due to a significantly higher proportion of trial-type 2 bigger than trial-type 3 for the participants who started with the inconsistent block, contrasted with an absence of difference for those who started with the consistent block. Comparisons of mean DIRAP scores corroborated this conclusion: for participants who started with the inconsistent block, there was strong evidence for trial-type 2 bigger than trial-type 3, but not for those who started with the consistent block. Finally, DTTTE had a significant main effect regardless of whether participants did or did not maintain the performance criteria at the trial-type level, with no interaction and no specific difference for those two groups.
These results highlight the importance of studying the influence of functional properties of stimuli. In other words, it emphasises the relevance of including a function-to-relation approach by using the DAARRE framework, and indeed RFT, to interpret behavioural data, in addition to the traditional relation-to-function approach. We have relied on a “nearest Cfunc coherence” response bias explanation for the DTTTE, and we have considered the extent to which maintaining performance criteria could reduce the STTDE. We have considered how future research on socially sensitive, evaluative responding may be informed by our findings. We conclude that the DAARRE model, expanded to accommodate block order and trial-type performance as relevant factors, is a promising framework for analysing the dynamics of arbitrarily-applicable relational responding in the environment of the IRAP.